Use the image to answer the question.
An illustration shows a triangle with sides measuring 16 meters, 14 meters, and 8 meters. A dashed perpendicular line, from the side measuring 16 meters to the opposite angle, measures 7 meters. A right angle symbol is shown to the left of the perpendicular line.
A prism and pyramid have congruent triangular bases. If their heights are both 15 m, what is the volume of each shape? (1 point)
The volume of a triangular pyramid is one-third of the volume of a triangular prism with the same base and height.
Therefore, the relationship between the volume of the pyramid and prism is:
Volume of pyramid : Volume of prism = 1 : 3
This ratio represents the fact that the volume of the pyramid is one-third of the volume of the prism.
If the volume of the pyramid is 48 in^3 and the prism and pyramid have congruent bases and the same height, then the volume of the prism would be three times that of the pyramid, as discussed in the previous response.
So, if the volume of the pyramid is 48 in^3, the volume of the prism would be:
48 in^3 * 3 = 144 in^3
Therefore, the volume of the prism is 144 in^3.
We know that the volume of the pyramid is 20 cm^3 and the base area of both the prism and pyramid is 15 cm^2.
Let's denote the height of the pyramid as h. We can write the volume formula for a pyramid as:
Volume = (1/3) * Base Area * Height
20 = (1/3) * 15 * h
60 = 15h
h = 60 / 15
h = 4
Therefore, the height of the rectangular prism is 4 cm.
The volume of a prism or pyramid can be calculated using the formula: Volume = (1/3) * Base Area * Height.
First, we need to calculate the area of the triangular base of the prism or pyramid. The area of a triangle can be calculated using the formula: Area = (1/2) * base * height.
Given that the base of the triangle is 16 meters and the height is 7 meters, we can calculate its area:
Area = (1/2) * 16 * 7 = 56 square meters.
Now we can calculate the volume of the prism and pyramid:
Volume = (1/3) * 56 * 15 = 280 cubic meters.
Therefore, the volume of both the prism and pyramid is 280 cubic meters.
The volumes of the pyramid and prism have to be separate.
Apologies for the confusion.
For the prism, we have already calculated the area of the triangular base to be 56 square meters.
Now we can calculate the volume of the prism using the formula: Volume = Base Area * Height.
Volume = 56 * 15 = 840 cubic meters.
For the pyramid, the base area is the same as the prism (56 square meters). Therefore, the volume of the pyramid would be:
Volume = (1/3) * Base Area * Height = (1/3) * 56 * 15 = 280 cubic meters.
Therefore, the volume of the prism is 840 cubic meters, and the volume of the pyramid is 280 cubic meters.
Thank you for clarifying the answer.
You're welcome! If you have any more questions or need further clarification, feel free to ask.
Given a triangular pyramid and triangular prism with congruent bases and the same heights, what do you know about the relationship between the volume of each? Write your answer in fraction form.
(1 point)
There is a rectangular prism and pyramid with congruent bases and height. If the volume of the pyramid is 48 in.3 , what is the volume of the prism?
(1 point)